Tasmania's Council on the Ageing says it has been blindsided by cuts to dementia funding.

On Thursday, the Federal Government announced it would no longer fund the Dementia and Severe Behaviours Supplement, citing a cost blowout.

It argued the former Labor government budgeted $11.7 million per year for the supplement, but the Government anticipates the cost will be around $110 million because of underestimates on how many people would be eligible.

The council's Sue Leitch hoped COTA Australia could work with the Federal Health Minister to look at alternatives for the funding.